As solid catalysts for olefin oligomerization, there are known solid acid catalysts, such as solid phosphoric acid, silica alumina and zeolite, and catalysts wherein a transition metal is supported on silica, alumina, silica.cndot.alumina or active carbon (see: "Industrial Catalyst Reaction I", Catalyst Course Vol. 8, 1985, published by Kodansha, "Catalyst Reaction (3), Polymerization", Catalyst Industrial Course Vol. 8, 1977, published by Chijinshokan).
Examples of olefin oligomerization processes using catalysts having alumina or silica alumina as a carrier include: a process using a catalyst wherein nickel sulfide is supported on a carrier of silica, alumina or silica.cndot.alumina, as described in Japanese Patent Publication No. 3489/1974; a process using a catalyst wherein nickel oxide and cobalt sulfate and/or magnesium sulfate are supported on alumina, as described in Japanese Patent Publication No. 30044/1975; a process using a nickel oxide-aluminum phosphate catalyst containing a small amount of alumina, silica or silica.cndot.alumina, as described in Japanese Patent Publication No. 30046/1975; and a process using a catalyst obtained by allowing a carrier of alumina, silica or silica.cndot.alumina to support thereon a nickel compound capable of being converted into nickel oxide by calcining and any of nitrate, sulfate and halide of a metal selected from Ca, Mg, Cd, Co, Zn, Al, Fe, Zr and Mn, or sulfate or halide of Ni, followed by calcining at 300.degree. to 700.degree. C., as described in Japanese Patent Laid-Open Publication No. 85506/1973.
Further, there have been proposed the following processes: an olefin oligomerization process using a catalyst wherein Ni.sup.2+ cation is introduced into silica.cndot.alumina by means of cation exchange, as described in Japanese Patent Laid-Open Publication No. 143830/1985; and a C.sub.2-6 olefin oligomerization process using a catalyst obtained by treating a supported composition wherein an oxide of a transition metal (M) selected from Ni, Co, Cr and Pd is supported on an acid oxide (e.g., alumina, silica.cndot.alumina, zeolite, diatomaceous earth, silica.cndot.titania and silica.cndot.magnesia), with a halogen-containing alkylaluminum compound, the atomic ratio of Al derived from the aluminum compound to the transition metal M (Al/M) being 0.5 to 10, as described in Japanese Patent Laid-Open Publication No. 151136/1986.
Furthermore, there are known other olefin oligomerization processes, such as a process in which a C.sub.4-10 olefin-containing raw material is brought into contact with amorphous silica.cndot.alumina having an alumina content of 10 to 50% by weight, a surface area of 50 to 600 m.sup.2 /g and a mean pore diameter of 10 to 100 .ANG. under the reaction conditions of a temperature of 150.degree. to 400.degree. C. and a pressure of 30 to 100 kg/cm.sup.2 -G, as described in Japanese Patent Publication No. 434/1993; a process in which a C.sub.4-10 olefin-containing raw material is brought into contact with a catalyst having 0.1 to 5.0% by weight of a rare earth metal supported on amorphous silica.cndot.alumina, as described in Japanese Patent Publication No. 39412/1994; and a process in which a material containing a C.sub.4 olefin of normal structure as its main component is subjected to a reaction by the use of a nickel oxide support type catalyst obtained by impregnating silica.cndot.alumina, which has been preliminarily heat treated at not lower than 600.degree. C., with a nickel salt solution to allow the silica.cndot.alumina to support 3 to 15% by weight (in terms of Ni) of nickel oxide, under the reaction conditions of a temperature of 50.degree. to 200.degree. C., a pressure of 20 to 100 kg/cm.sup.2 -G and LHSV of 0.1 to 5.0 hr.sup.-1, to obtain a C.sub.8 olefin having a degree of branching of not higher than 1.5, as described in Japanese Patent Laid-Open Publication No. 287227/1994.
These conventional catalysts, however, are not always satisfactory in oligomerization of an olefin due to their poor selectivity of dimerization and low activity. In addition, when an olefin oligomer is used, for example, as material for a phthalic acid plasticizer to be blended with polymer such as polyvinyl chloride, the olefin oligomer is desired to have a low degree of branching, i.e., few side chains. The above conventional process, however, are not always successful in obtaining a desired olefin oligomer having a sufficiently low degree of branching.